Chapter 13, Problem 1RE

To determine

Whether the statement “$y=-6^{-x}$ is an exponential function” is true or false.

Answer to Problem 1RE

The statement is $\underset{\_}{\text{true}}$.

Explanation of Solution

Definition used:

The exponential function is defined as $y=b^x$, where $b>0,b\ne 1$ and x is any real number.

Calculation:

Rewrite the equation $y=-6^{-x}$ as $y=\left(-1\right)6^{-x}$.

Note that, $y=\left(-1\right)6^{-x}$ is of the form $y=b^x$ where $b=6,x=-x$.

Hence, the equation satisfies the condition $b>0,b\ne 1$.

Therefore, the statement is $\underset{\_}{\text{true}}$.